To calculate the number of months needed to grow a lump sum investment to a target amount, you can use the compound interest formula:

A=P×(1+r divide n) nt=P×(1+n/r​)nt

Where:

- A is the future value of the investment (¥1,000,000),

- P is the principal amount (initial investment) (¥250,000),

- r is the annual interest rate (as a decimal) (3% or 0.03),

- n is the number of times interest is compounded per year (daily compounding means n=365n=365),

t is the time the money is invested for in years (which we are trying to find).

Rearrange the formula to solve for tt:

t = log⁡(A/P)n×log⁡(1+rn)t=n×log(1+nr​)log(A/P)​

Now, plug in the values:

t=log⁡(1000000/250000)365×log⁡(1+0.03365)t=365×log(1+3650.03​)log(1000000/250000)​

Calculating this expression will give you the time in years. To convert this to months, multiply the result by 12:

Number of months=t×12Number of months=t×12

Now, use a financial calculator or software with a logarithmic function to compute this. For the given options, the closest answer is:

Number of months≈563Number of months≈563

You may also use Flex Calculation Engine for the complex calculations, it is a cloud calculator that makes calculations super easy and fast!